Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+5y &= -8 \\ 7x+3y &= -9\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -7x-9$ Divide both sides by $3$ to isolate $y$ $y = {-\dfrac{7}{3}x - 3}$ Substitute this expression for $y$ in the first equation. $-7x+5({-\dfrac{7}{3}x - 3}) = -8$ $-7x - \dfrac{35}{3}x - 15 = -8$ Simplify by combining terms, then solve for $x$ $-\dfrac{56}{3}x - 15 = -8$ $-\dfrac{56}{3}x = 7$ $x = -\dfrac{3}{8}$ Substitute $-\dfrac{3}{8}$ for $x$ back into the top equation. $-7( -\dfrac{3}{8})+5y = -8$ $\dfrac{21}{8}+5y = -8$ $5y = -\dfrac{85}{8}$ $y = -\dfrac{17}{8}$ The solution is $\enspace x = -\dfrac{3}{8}, \enspace y = -\dfrac{17}{8}$.